Find the directional derivative of f at the given point in the direction indicated by the angle θ. f(x, y) = y cos(xy), (0, 1), θ = π/6

Step-by-step explanation:

The directional derivative of f at the given point in the direction indicated by the angle θ is expressed as where u is the unit vector in the direction θ.

Lets first calculate

The unit vector u in the direction of θ  is expressed as

unit vector u  at θ = π/6 is cos π/6i + sin π/6 j

u= √3/2 i +1/2 j

Taking the dot product i.e

= (0i+j)*(√3/2 i +1/2 j)

= 1/2

The directional derivative of f is 1/2

-1/2 +2

step-by-step explanation: